Workshop on the ramification theory for varieties over a local field I

30-31 December 2022, online workshop

In these series of workshops, we aim to study the conductor formula for constructible sheaves on regular schemes over a local ring.

Organizers

Fangzhou Jin, Peng Sun, Enlin Yang, Yigeng Zhao
This workshop is supported by the National Key Research and Development Program of China Grant Nr.2021YFA1001400 and the NSFC Grants Nr.11901008 and 12271006.

Speakers

Haoyu Hu
Fangzhou Jin
Peng Sun
Yupeng Wang
Qin Xue
Enlin Yang
Yigeng Zhao

Schedule

Tencent Meeting: 583-1580-8373 pw: 235711

December 30
09:00-10:00 Localized Chern classes and localized intersection product 1 (Jin)
10:15-11:15 Localized Chern classes and localized intersection product 2 (Jin) Notes
13:00-14:00 Conductor formula of Bloch 1 (Zhao)
14:15-15:15 Conductor formula of Bloch 2 (Zhao)
15:30-16:30 Deligne's conjecture on Milnor formula (Hu)
19:00-20:00 Frobenius-Witt differentials and cotangent bundle of regular schemes 1 (Xue)
December 31
09:00-10:00 K-theoretic localized Chern classes (Yang)
10:15-11:15 Conductor formula vs. Milnor formula 1 (Sun)
13:00-14:00 Conductor formula vs. Milnor formula 2 (Sun)
14:15-15:15 Extension of local fields 1 (Wang)
15:30-16:30 Extension of local fields 2 (Wang) Notes
19:00-20:00 Frobenius-Witt differentials and cotangent bundle of regular schemes 2 (Xue)

References:
[1] P. Deligne, La formule de Milnor, SGA 7, Expose XVI.
[2] J-P. Wintenberger, Le corps des normes de certaines extensions infinies de corps locaux; applications, Annales scientifiques de l'E.N.S. 4 serie, tome 16, n1(1983), p.59-89.
[3] S. Bloch, Cycles on arithmetic schemes and Euler characteristics of curves, Proc. Sympos. Pure Math. 46 (1987):421-450.
[4] F. Orgogozo, Conjecture de Bloch et nombres de Milnor, Annales de L'institut Fourier, Tome 53, n6(2003): 1739-1754.
[5] A. Abbes, Cycles on arithmetic surfaces, Composito Mathematica 122 (2000): 23-111.
[6] K. Kato and T. Saito, On the conductor formula of Bloch, Publ.Math.IHES,100(2005):5-151.
[7] K. Kato, and T. Saito, Ramification theory for varieties over a local field. Publ.math.IHES 117, 1-178 (2013).
[8] T. Saito, Frobenius-Witt differentials and regularity, Algebra and Number Theory 16: 2(2022), 369-391.
[9] T. Saito, Cotangent bundle and microsupports in the mixed characteristic case, Algebra and Number Theory 16: 2(2022), 335-368.